Boiler Circulation Calculations 6t4p5h

HEAT TRANSFER

Boiler circulation calculations Steam

Steam generator studies can be complex. Use these guidelines to perform them effectively V Ganapathy, ABCO Industries, Abilene, Texas

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Fig. 1. Schematic of a water tube boiler.

atural circulation water tube and fire tube boilers

(Figs. 1 and 2) are widely used in the chemi cal process industry. These are preferred to forced circulation boilers (Fig. 3) where a circulation pump ensures flow of a steam/water mixture through the tubes. In addition to being an operating expense, a pump failure can have serious consequences in such systems. The motive force driving the steam/water mixture through the tubes (water tube boilers) or over tubes (fire tube boilers) in natural-circulation systems is the difference in density between cooler water in the downcomer circuits and the steam/water mixture in the riser tubes. This flow must be adequate to cool the tubes and prevent overheating. This article explains how circulation ratio or the ratio of steam/water mixture to steam flow may be evaluated. Circulation ratio (CR) by itself does not give a complete picture of the circulation system. Natural-circulation boiling circuits are in successful operation with CRs ranging from 4 to 8 at high steam pressures (1,500 to 2,100 psig) in large utility and industrial boilers. In waste-heat boiler systems, CR may range from 15 to 50 at low steam pres sures (1,000 to 200 psig). CR must be used in conjunction with heat flux, steam pressure, tube size, orientation, roughness of tubes, water quality, etc., to understand the bo iling process and its reliability. Tube failures occur due to conditions known as departure from nucleate boiling (DNB) when the actual heat flux in the boiling circuit exceeds a critical value known as critical heat flux-a function of the variables mentio ned above. When this occurs, the rate of bubble formation is so high compared to the rate at which they are carried away by the mixture that the tube is not cooled properly, resulting in overheating and failure.

deaerator. This mixes with the steam/ water mixture inside the drum. Downcomers carry the resultant cool water to the bottom of the evaporator tubes while external risers carry the water/steam mixture to the steam drum. The heat transfer tubes also act as risers generating steam. The quantity of mixture flowing through the system is determined by calculating the CR. This is a trial-and -error procedure and is quite involved when there are multiple paths for downcomers, risers and evaporator circuits. Each boiling circuit has its own CR depending on the steam generated and system resistance. One can split up any evaporator into various parallel paths, each with its own steam generation and CR. Splitting up is done based on judgment and experience. A particular circuit may be examined in detail if the process engineer feels that it offers more resistance to circulation or if it is exposed to high heat flux conditions. Several low heat flux circuits can be clubbed into one circuit to reduce computing time. Hence, an average CR for the entire system does not give the complete picture. Circulation ratio. CR is defined as the ratio of the mass of steam/water mixture to steam generation. The mass of the mixture flowing in the system is determined by balancing the thermal head available with various system losses, including: • Friction and other losses in the downcomer piping, including bends Two -phase friction, acceleration and gravity losses in the heated riser tubes Continued

Circulation process. Fig. 1 shows a typical water-tube, natural-circulation waste -heat boiler with an external steam drum and external downcomers and riser pipes. Feed water enters the drum from an economizer or HYDROCARBON PROCESSING/ JANUARY 1998

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• Friction and other losses in the external riser piping • Gravity loss in the riser piping • Losses in drum internals. COMPUTING THE VARIOUS LOSSES Total thermal head. The total thermal head available

in psi = H/vl/144 where H is the thermal head, ft (Fig. 1) vl is the specific volume of 3 water, ft /lb Downcomer losses. Let the average CR for the system = CR and the total steam generation = WS lb/hr. The total mixture flowing through the system = W S x CR Let the effective length (including bends) of the downcomer piping in ft = L e The frictional pressure drop, psi = 3.36 X 10-s x f 2 5 Le vi (W d) /di (Here, it is assumed that the average flow in each downcomer pipe is W d ). d i is the inner diameter of the downcomer pipe in inches. f is the friction factor. If there are several parallel paths or series -parallel paths, then the flow and pressure drop in each path is determined using electrical analogy. This calculation may require a computer. In addition to the frictional drop, the inlet (0.5 x velocity head) and exit losses (1 X velocity head) must be computed. Sometimes the pipe inner diameter is larger than the inner diameter of the nozzle at the ends, in which case the higher velocity at the nozzles must be used to compute the inlet/exit losses. Velocity V in ft /s = 0.05 Wd 2 v l/die and velocity head, psi = V /2 g vl/144. Heated riser losses. The boiling height must first be

determined. This is the vertical distance the mixture travels before the boiling process begins. It can be shown by calculation that the mixture's enthalpy entering the evaporator section is usually less than that of saturated liquid. The following is the energy balance around the steam

Fig. 3. A forced-circulation system showing multiple streams to reduce pressure drop.

Steam drum, as in Fig. 1: Wmh+W f hf =Wmh m+W s h„ Wm = mixtureflowing through the system, lb/hr =Ws x CR hv, hm, hf, and h are the enthalpies of saturated steam mixture leaving the drum, feed water entering the drum and mixture leaving the drum, Btu/lb.

h=(hv/CR)+(1-1/CR)hl where hv, h j = enthalpies of saturated vapor and liquid, Btu/lb. From the above, hm is solved for. The boiling height or the distance the mixture travels before boiling starts, Hb, is determined from: Hb = He X W S X CR X (hl - hm)/Qs where He = height of evaporator tubes, ft (For conservative calculations, Hb may be assumed to be zero.) There are basically three losses in boiling evaporator tubes: Friction loss. -1 0 2 ∆pf= 4 X 10 vl X f L X Gi X r3/di where Gi= mixture mass velocity inside tubes, 2 lb/ft hr f= fanning friction factor L= effective length, ft di= tube inner diameter, in. r3= Thom's multiplication factor for twophase friction loss (Fig. 4a). Gravity loss in tubes. ∆Pg = 0.00695 (He - Hb) r4/v1 Thom's multiplication factor for gravity loss, r4 is shown in Fig. 4c.

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Fig. 4. Thom's two-phase multiplication factors for: a) friction loss, b) acceleration loss, and c) gravity loss.

Acceleration loss. ∆pQ=1.664x10-11x vlXGi2 xr2 where r2, Thom's multiplication factor, is shown in Fig. 4b. External riser losses. These are similar to the downcomer losses except that the specific volume is that of the mixture and not saturated liquid. Mixture specific volume v„,, ft 3/lb, is computed as: vm = vs/CR + (1- 1/CR) v l Riser gravity loss. ∆p, = (H - He)1vm/144 where vm is the specific volume of the mixture. Losses in drum internals. These usually consist of losses in the baffles and cyclones if used and range from 0.2 to 1 psi. Total losses are calculated and balanced against the thermal head available. If they balance, the CR assumed is correct, otherwise, the iteration is repeated by assuming another CR until the losses balance with the head available. When there are several boiling circuits, one can split up the total steam flow based on steam generation in each circuit until the losses balance. A simple manual procedure is to compute losses in the circuits as a function of flow and see where it intersects the available head line, Fig. 5. Since the available head and pressure drops in the riser and downcomer system are same for all the evapo

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Table 1: Boiler data for circulation study Duty, Steam Gas Rows Surface, Fins/in x height x thickness MMBtu/hr flow, temp, 2 1-4 691 bare 11.5 11,500 1,650 5-7 2,967 2.5 x 0.75 x 0.075 27.1 27,000 1,500 8-20 20,216 4.5 x .75 x .05 39.0 39,000 1,130 Riser 3. 8 in., 8-ft long, 2 bends Downcomers: 2. 6 in., 24-ft long, s: 8 in., 12-ft long, 4 bends 6 in., 26-ft2long, 8 in., 8-ft long, 2 bends 3 Steam pressure = 645 psia. Total head =18 ft. Drum internal loss Evaporator tube ID =1.738 in length=11 ft.

rator circuits, this graphical method is sometimes used, although it is tedious. If the downcomer or external riser piping consists of several parallel or parallel-series paths, the electrical analogy is used to determine flow and pres sure drop in each circuit. A computer program best handles this problem. EXAMPLE CALCULATION

Fig. 1 is a waste-heat boiler operating under the following conditions: Gas flow = 200,000 lb/hr Gas inlet temperature = 1,650°F (vol% C02 =7, H2O = 18, N2 = 69, 02 = 6) Steam pressure = 500 psia Feed water temperature = 230°F The total steam generated is 63,5001b/hr. The first four rows are bare, followed by six finned tubes and then 10 more with higher fin density. Details of downcomers, riser pipes and other pertinent information are in Table 1. Determine the system's circulation ratio and the flow in each pipe circuit. Note that the boiler design calculations must be done before circulation studies can be taken up. Also, one must have a good feel for the downcomer and riser pipe sizes and their layout. Often piping layout is changed at the last moment to accommodate other equipment in the plant without reevaluating circulation. A computer program was developed to perform this analysis. The evaporator 4 HYDROCARBON PROCESSING / JANUARY 1998

Heat flux, Btu/ft 2-hr 20,500 83,000 58,000 bends bends

streams or paths for evaluating circulation, even though the program can analyze more circuits. Results are shown in Table 2. Analysis of results . Boiler heat -

transfer calculations have to be done before a circulation study can be undertaken. The maximum steam 0.3 psi. generation case is usually evaluated. The heat -transfer calculations give the steam generation, flux tube and gas temperatures in each section. heat In water boilers, the heat flux inside the tubes is computed, while in fire tube boilers the heat flux outside the tubes is important. For water tube boilers, heat flux, q = Uo x ( t g - ts) x At /Ai ,Where Uo = overall outside heat -transfer 2 coefficient, Btu/ft -hr-°F t g, i s are gas and steam temperatures, °F At , Ai are the tube outside and inside surface areas, 2 ft /ft. This ratio is for bare tubes, while for finned tubes it could be high, say 5 to 12. Hence, one must be careful while analyzing finned tube bundles, as the heat flux can be very high inside the tubes. In fire tube boilers, q = Uo x ( t g - ts) Based on preliminary analyses, the CR in each circuit and overall basis seems to be reasonable. The maximum heat flux at the inlet to each section is in Table 1. Correlations are available in the literature for allowable heat flux as a function of pressure, quality and tube size, etc. These are mostly based on experimental data conducted in laboratories and are often used for guidance only. The actual permissible heat fluxes are much lower and are based on industry experience and could be 10% to 30% of the values given in correlations in handbooks. Vertical tubes can handle much higher heat fluxes than horizontal tubes, up to 40% to 50% more. Limits of 2 120,000 to 175,000 Btu/ft -hr inside tubes are permitted at pressures ranging from 1,000 to 2,000 psig, while in fire 2 tube boilers the limit is around 100,000 Btu/ft -hr. The higher the steam pressure, the lower the allowable heat flux. Similarly, the higher the steam quality (lower CR), the lower the allowable heat flux. As the CR increases, the quality decreases and higher fluxes are permissible. With higher flow, the tube periphery is wetted better and is considered safer. Another approach that is widely used is the comparison between allowable steam quality and actual steam quality. Fig. 6 shows a radiant boiler furnace, where the steam quality, x, (x=1/CR) is plotted against the height. Based on heat flux distribution along the height, the allowable quality is calculated using a correlation similar to that shown below. The allowable and actual steam qualities should be apart in order to avoid DNB problems. This type of analysis is similar to that using allowable and actual heat fluxes. The McBeth correlation shown below shows the relation among the variables involved in boiling inside vertical 1 tubes: 6 -0.1 6 0.51 q, = 0.00633 x 10 x hfg di (Gi/10 ) x (1-x) 2 where q, =critical heat flux, Btu/ft -hr h f g= latent heat of steam, Btu/lb

Fig. 6. Actual vs. allowable quality and heat flux variation with furnace height.

x= steam quality, fraction (x = 1/CR) 2 Gi Gi= mass velocity lb/ft -hr di = tube inner diameter, in. For example, the critical heat flux at a steam pressure of 1,000 psi (latent heat = 650 Btu/lb), di = 2 1.5 in., Gi = 600,000 lb/ft -hr and x = 0.2 is: 6 -0.1 51 qa = 0.00633 x 10 x 650 x 1.5 x 0.6° (1-0.2) 6 2 = 2.43 x 10 Btu/ft -hr. As discussed earlier, the above equation may be used to study the effect of various variables involved and not for determining critical heat flux. Actual allowable critical heat fluxes are much lower on the order of 10% to 30% of the above value. Fire tube boilers. A similar procedure may be adopted for fire tube boilers, Fig. 2. The frictional losses in the evaporator section are usually small. The heat flux at the tube sheet inlet is high and must be considered. CR ranges from 15 to 30 due to the low steam pressures compared to water tube boilers. Generally, there is only one evaporator circuit. The correlation for allowable heat 1 flux by Motsinki is: 0.35 0.9 qc = 803 Pc x (P s /Pe) x (1 -Ps /Pc ) Where PS and Pc are steam pressure and critical pres sure of steam, psia. At 400 psia, qc = 803 x 3,208 x 0.35 0 9 6 2 (400/3,208) x (1- 400 / 3,208) . = 1.1 x 10 Btu/ft -hr. As mentioned earlier, the actual allowable flux would be 10% to 30% of this value. Forced-circulation boilers. In forced-circulation systems, the losses are determined as indicated above. However, the available head is generally too small, so a circulating pump is added (Fig. 3) to ensure desired CR. The CR may be selected unlike in a natural-circulation system, where it is arrived at through an iterative process. If the evaporator circuits are of different lengths then orifices may also be added inside tubes to ensure flow stability. CR could range from 2 to 6 in such systems to reduce operating costs. Pump reliability is a must. In gas turbine HRSGs that use horizontal tubes, the pressure drop inside tubes is

quite high compared to vertical tubes used in naturalcirculation boilers. To reduce the pressure drop, multiple streams could be considered as shown or the pump may be eliminated by locating the drum sufficiently high, resulting in a naturalcirculation system.Final thoughts. Circulation studies are complex and preferably done using a computer. The analysis of results requires experience and is generally based on from operation of similar boilers in the field. Specifying a minimum CR for a boiler is not the right approach since CR varies with different circuits. One has to review the heat fluxes and steam quality at various points in the system to see if there could be problems. Some evaporator circuits could be more critical than others and require careful analysis. For example, Fig. 7 shows the front wall of a packaged water tube boiler with completely watercooled furnace design. This wall has basically two parallel flow systems between the bottom mud drum and the steam drum, namely the tubes that connect the bot tom header to the top header and the header itself, which has an L-shape. Flow calculations were done and orifices were used to ensure proper flow distribution in all the heated circuits. LITERATURE CITED Ganapathy, V, Steam plant calculations manual, 2nd edition, Marcel Dekker, New York, 1994. 2 Thom, J. R. S., "Prediction of pressure drop during forced circulation boiling of water," International Journal of Heat Transfer No. 7, 1964. 3. Roshenow, W, and J. P. Hartnett, Handbook of heat transfer, McGraw-Hill, 1972. 1

The author:V. Ganapathy is a heat transfer specialist with ABCO Industries Inc., Abilene, Texas. He is engaged in the engineering of heat recovery boilers for process, incineration and cogeneration applications and packaged water tube steam generators. He also develops software for engineering of heat recovery systems and components. He holds a B Tech degree in mechanical engineering from Indian Institute of Technology, Madras, India, and an MSc(eng) in boiler technology from Madras University. Mr. Ganapathy is the author of over 175 articles on boilers, heat transfer and steam plant systems and has written five books: Applied Heat Transfer, Steam Plant Calculations Manual, Nomograms for Steam Generation and Utilization, Basic Programs for Steam Plant Engineers (book and diskette), and Waste Heat Boiler Deskbook, copies of which are available from him. He also has contributed several chapters to the Encyclopedia of Chemical Processing and Designs, Vols. 25 and 26, Marcel Dekker, New York.